We search the five CANDELS fields (COSMOS, EGS, GOODS-North, GOODS-South and UDS) for passively evolving a.k.a. "red and dead" massive galaxies in the first 2 Gyr after the Big Bang, integrating and updating the work on GOODS-South presented in a previous paper. We perform SED-fitting on photometric data, with top-hat star-formation histories to model an early and abrupt quenching, and using a probabilistic approach to select only robust candidates. Using libraries without (with) spectral lines emission, starting from a total of more than 20,000 z > 3 sources we end up with 102 (40) candidates, including one at z = 6.7. This implies a minimal number density of 1.73 ± 0.17 × 10-5 (6.69 ± 1.08 × 10-6) Mpc-3 for 3 < z < 5; applying a correction factor to account for incompleteness yields 2.30 ± 0.20 × 10-5. We compare these values with those from five recent hydrodynamical cosmological simulations, finding a reasonable agreement at z < 4; tensions arise at earlier epochs. Finally, we use the star-formation histories from the best-fit models to estimate the contribution of the high-redshift passive galaxies to the global Star Formation Rate Density during their phase of activity, finding that they account for ̃5-10% of the total star formation at 3 < z < 8, despite being only ̃ 0.5% of the total in number. The resulting picture is that early and strong star formation activity, building massive galaxies on short timescales and followed by a quick and abrupt quenching, is a rare but crucial phenomenon in the early Universe: the evolution of the cosmos must be heavily influenced by the short but powerful activity of these pristine monsters.